Biomedical Engineering Reference
In-Depth Information
Chapter 2
Fractal Characterization of Complexity in Dynamic Signals:
Application to Cerebral Hemodynamics
Peter Herman, Laszlo Kocsis, and Andras Eke
Abstract
We introduce the concept of spatial and temporal complexity with emphasis on how its fractal character-
ization for 1D, 2D or 3D hemodynamic brain signals can be carried out. Using high-resolution exper-
imental data sets acquired in animal and human brain by noninvasive methods - such as laser Doppler
flowmetry, laser speckle, near infrared, or functional magnetic resonance imaging - the spatiotemporal
complexity of cerebral hemodynamics is demonstrated. It is characterized by spontaneous, seemingly
random (that is disorderly) fluctuation of the hemodynamic signals. Fractal analysis, however, proved
that these fluctuations are correlated according to the special order of self-similarity. The degree of cor-
relation can be assessed quantitatively either in the temporal or the frequency domain respectively by
the Hurst exponent (
H
) and the spectral index (
). The values of
H
for parenchymal regions of white
and gray matter of the rat brain cortex are distinctly different. In human studies, the values of
β
were
instrumental in identifying age-related stiffening of cerebral vasculature and their potential vulnerability
in watershed areas of the brain cortex such as in borderline regions between frontal and temporal lobes.
Biological complexity seems to be present within a restricted range of
H
or
β
β
values which may have
medical significance because outlying values can indicate a state of pathology.
Key words:
Complexity, fractals, laser Doppler flowmtery, laser speckle imaging, MRI, cerebral
blood flow.
1. Introduction
The human brain represents the highest degree of organization of
matter and is often referred to as being “hypercomplex”
(1)
.The
brain's hypercomplexity does not only reflect its assembly consist-
ing of astronomical number of neurons
(2)
capable of operating
in concert to produce various functions of the nervous system, but
also highlights the fact that traditional approaches and available
